5.2 Plasma Density Peak in the Afterglow
5.2.2 Pooling Ionization
−200 0 200 400 600 800 1000
−10 0 10 20 30 40 50 60 70
Time (µs)
Ion Saturation Current (mA)
B on
z = −7.3 cm pH
2
= 0 mTorr pH
2
= 20 mTorr
pH
2
= 80 mTorr
−200 0 200 400 600 800 1000
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (µs)
Ion Saturation Current (mA)
B on z = 6.0 cm
pH
2
= 0 mTorr pH
2
= 20 mTorr
pH
2
= 40 mTorr
Figure 5.12: Ion saturation current inside the RF antenna (left) and out in the main vacuum chamber (right) during experiments with a uniform hydrogen backfill and argon supplied to the RF discharge tube using the fast gas valve (Vgas,RF = 550 V). The RF power was turned on fromt= 0–500µs, and the bias magnetic field was applied (Vbias= 80 V, Vsol.= 0 V).
density increases of up to an order of magnitude in argon discharges.
In order to test whether pooling ionization could be responsible for the afterglow density rise in our RF discharge, we tried introducing various amounts of hydrogen gas into the chamber while also supplying argon to the RF discharge tube using the fast gas valve.
Kenty [111] suggested that the presence of H2 in an argon discharge will tend to depopulate the Ar metastable state, a fact that was confirmed in more recent numerical simulations by Bogaerts [123], who found that adding a hydrogen concentration of only 5% to a glow discharge with pAr = 560 mTorr reduced the peak nm by a factor of ∼ 10. The rate coefficients for de-excitation of an argon metastable by collisions with an H2 molecule or H atom are kH2 ≈10−16 m3/s andkH ≈2×10−16 m3/s, respectively [124]. Therefore, with a hydrogen partial pressure of 30 mTorr (nH2 = 1021 m−3), the mean lifetime of an argon metastable atom is<10µs.
The results of the experiments with argon-hydrogen6mixtures are shown in Fig. 5.12. In the left panel, we see that adding hydrogen to the argon discharge moderately decreased the plasma density inside the antenna, but the time-dependence remained largely unchanged.
Out in the main chamber, however, there were more drastic effects (right panel), probably
6A gas species correction factor of 0.4 was applied to the hydrogen pressures measured by the thermocou- ple gauge, based on calibration of the thermocouple for H2using a capacitance manometer from the Caltech ice dusty plasma experiment [86].
because the argon pressure produced by the fast gas valve was lower at this location and thus the relative hydrogen concentration was higher. The size of the afterglow density peak was smaller relative to the density prior to the rise withpH2 = 20 mTorr than it was with no hydrogen present, and withpH2 = 40 mTorr the afterglow density rise disappeared altogether. These results suggest that pooling ionization may have been responsible for the observed behavior in the afterglow. Experiments were also carried out in which the chamber was filled uniformly with argon at 0–40 mTorr before additional argon gas was supplied to the discharge tube using the fast gas valve. The afterglow density increase persisted, confirming that only a hydrogen gas fill would impede the effect.
From Fig. 5.8, the observed rate of increase of the ion density in argon afterglows was
∂ni/∂t∼1022m−3/s. Okada and Sugawara [125] measured the cross section for metastable- metastable ionization to be σmmi= 1.35×10−17 m2. Assuming a typical relative velocity vr = 500 m/s between the colliding metastable atoms (Tg ≈0.05 eV), the rate coefficient7 wasKmmi≈7×10−15m3/s. The pooling ionization rate per unit volume isKmmin2m, so in order to account for the measured∂ni/∂tin the afterglow, the metastable population density needed to benm ≈1018m−3. On the other hand, given that two metastables are destroyed in every pooling ionization reaction, an initial population density nm & 2×1018m−3 was required in order to ultimately increaseni by 1018 m−3 as in Fig. 5.8. These are plausible metastable densities, although larger than the downstream values of nm predicted by the 1D discharge model from Sec. 4.4.2 for uniform gas pressures below 300 mTorr (see Fig.
4.24).
A possible problem for the pooling ionization hypothesis is that the expected rate of destruction of metastable atoms appears to be too high to explain the data, even in pure argon discharges. The dominant loss process for metastables in the afterglow was electron- impact transitions to the 4sresonant state followed by radiative decay to the ground state;
the rate for the metastable-to-resonant transition was νmr = Kmrne, where Kmr = 2× 10−13 m3/s (see Table 3.1). Therefore, with ne ≈ 5×1017 m−3 (a typical value during the afterglow density rise—see the right panel of Fig. 5.8), the metastable lifetime was only
7Elsewhere in the literature [126, 127], a rate coefficientKmmi≈6×10−16m3/s for argon metastable- metastable ionization has often been adopted. However, this value was actually inferred from cross section measurements taken in other noble gases [128, 129] and thus it may not be accurate for argon.
νmr−1 ≈ 10 µs. However, the plasma density in the afterglow didn’t peak until ∼ 100 µs after RF turn-off, so some metastable atoms must have survived this long, if they were indeed responsible for the density increase (we have not identified any likely source of new metastables in the afterglow other than three-body recombination, which can be neglected in this discussion since recombination followed by pooling ionization did not lead to a net increase in the ion density). It is notable that all other instances of afterglow density rises due to pooling ionization that we know of [118, 119, 120, 121] occurred in plasmas with ne≤5×1016m−3, so the metastable lifetime in the afterglow was 100µs or longer.
Based on the results of experiments with argon-hydrogen mixtures shown in Fig. 5.12, it seems clear that atomic processes producing new ionization were the fundamental cause of the afterglow density rise in our RF discharge. However, the detailed sequence of processes involved, which may have been more complex than pooling ionization alone, remains to be conclusively determined. Preliminary numerical calculations were carried out in which pool- ing ionization terms were added to the 1D discharge model equations in Sec. 4.4.2: only very small afterglow density increases were observed in simulations of unmagnetized discharges with uniform gas pressure. This result is consistent with the data shown in Figs. 5.9 and 5.10, but calculations with nonuniform pressure and radial confinement will be required if the dramatic afterglow density peak observed in discharges with the bias field and fast gas valve used is to be reproduced. Direct measurements of the time-dependent metastable den- sity (for example, using laser absorption) would be very valuable for confirming or refuting the proposed pooling ionization mechanism.